Take, as an example, a system consisting of two celestial bodies where both bodies turn around the bury-center, a center of masses of two bodies, taking a circular orbit like the Earth and the Sun, and a vary light third body flying in the system. It has been known that there are five equilibrium points in the system where gravity from those two bodies and a centrifugal force acting on a third body are balanced. They are known as Lagrange points. The practical implication of the Lagrange points has been studied for a long time. Among the five equilibrium points, Lagrange points, the points L1 and L2 allow a spacecraft, a third body, to be comparatively easily accessed because there the pseudo potential is relatively low. In view of this, this invention attempts an observatory or a space dock spacecraft to be stationary on the point in order to extract the merit that the position and the geometry of the observatory or the dock is frozen with respect to the Sun or the Earth.
As stated above, although accessing and positioning to/at the point L1 or L2 are easier than those to/at the other Lagrange points, it does not readily mean that placing a spacecraft on the point is easy without any consideration about the initial conditions around the point. For example, initial conditions corresponding to divergent motion that may occur around the point must be avoided deliberately. The orbits around L1 or L2, if those improper divergent motions are eliminated, are basically stable and seem suitable for the purposes discusses here. The characteristic frequency of the orbital motion around the point L1 or L2 takes different values for in-plane and out-of-plane directions. Accordingly, while the orbit of the spacecraft is stable, usually it does not draw a closed locus, but takes a so-called Lissajous locus.
When a spacecraft takes a Lissajous orbit around the point L2, the orbit may be shadowed by the Earth. And when a spacecraft takes a Lissajous orbit around point L1, the ground station will see the Sun behind the spacecraft and the communication between the ground stations and the spacecraft may be disturbed significantly. These problems have prevented the use of the L1 or L2 point, and also have not realized the spacecraft on the above-mentioned Lissajous orbit around the Lagrange points L1 or L2.
By the way, it has been revealed by previous studies that if a Lissajous orbit is enlarged to a much more large scale one to enter into a non-collinear area, the non-linear effect makes the spacecraft trajectory closed. And the orbit of a spacecraft, if the spacecraft is positioned close to point L2, can avoid shadow by the Earth, and if the spacecraft is positioned close to point L1, can avoid passage in front of the Sun. When viewed from the Earth, it looks like a halo around the Sun, and thus it is called a halo orbit.
Following patent documents deal with the orbits around the Lagrange points and the halo orbits, i.e., U.S. Pat. Nos. 6,809,818; 6,385,512; 4,795,113; and 5,183,225.